Question 499106: The length of one leg of a right triangle is 3 centimeters more than the length of the other leg. The length of the hypotenuse is 15 centimeters. Find the lengths of the two legs.
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! Using the Pythagorean Theorem, we know that
c^2 = a^2 + b^2
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c^2 = 15^2
c^2 = 225
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a = b+3
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a^2 + b^2 = 225
(b+3)^2 + b^2 = 225
(b+3)(b+3) + b^2 = 225
Use FOIL on the first term.
b^2 +3b +3b + 9 +b^2 = 225
Collect terms.
2b^2 +6b + 9 = 225
Subtract 225 from both sides
2b^2 +6b -216 = 0
Divide both sides by 2 to eliminate the coefficient on b^2.
b^2 +3b -108 = 0
Factor
(b+12)(b-9) = 0
So, b=-12 or b=9.
A negative length does not make sense, so b=9.
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Use the Pythagorean to find side a.
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a^2 = c^2 - b^2
a^2 = 225 - 81
a^2 = 144
a = 12
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So, the lengths of the two legs are 9 cm and 12 cm.
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Done.
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